Office Applications and Entertainment, Magic Cubes  
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7.0 Special Cubes, Prime Numbers
7.7 Associated Magic Cubes (5 x 5 x 5)
Associated Magic Cubes of order 5 can be considered as being composed out of an Associated Border and a (non magic) Associated Inner Cube.
7.7.2 (Semi) Magic Surface Planes
Associated Magic Cubes can be constructed based on
Complementary Anti Symmetric Magic Squares of order 5, as discussed in Section 14.3.10.
The relation between opposite surface squares (symmetry) can be represented as follows:
with Pr5 = 2 * s5 / 5 the pair sum for the corresponding Magic Sum s5.
the defining equations of the Back Square (Semi Magic) can be written as: a( 6) = s5  a(11)  a(16)  a( 1)  a(21) a( 7) = s5  a(12)  a(17)  a( 2)  a(22) a( 8) = s5  a(13)  a(18)  a( 3)  a(23) a( 9) = s5  a(14)  a(19)  a( 4)  a(24) a(10) = s5  a(15)  a(20)  a( 5)  a(25) a(11) = s5  a(12)  a(13)  a(14)  a(15) a(16) = s5  a(17)  a(18)  a(19)  a(20)
with a(i) independent for i = 12 ... 15 and i = 17 ... 20;
the defining equations of the Left Square (Semi Magic) can be written as: a( 7) = s5  a(12)  a(17)  a( 2)  a(22) a( 8) = s5  a(13)  a(18)  a( 3)  a(23) a( 9) = s5  a(14)  a(19)  a( 4)  a(24) a(12) = s5  a(13)  a(14)  a(11)  a(15) a(17) = s5  a(18)  a(19)  a(16)  a(20)
with a(i) independent for i = 13, 14, 18 and 19; c(92) = s5  c(91)  c(93)  c(94)  c(95) c(84) = s5  c(79)  c(89)  c(94)  c(99) c(87) = s5  c(86)  c(88)  c(89)  c(90) c(83) = s5  c(78)  c(88)  c(93)  c(98) c(82) = s5  c(81)  c(83)  c(84)  c(85) c(69) = s5  c(19)  c(44)  c(94)  c(119) c(68) = s5  c(18)  c(43)  c(93)  c(118) c(67) = s5  c(17)  c(42)  c(92)  c(117) c(64) = s5  c(14)  c(39)  c(89)  c(114)
with c(i) independent for i = 88, 89, 93 and 94;
Attachment 7.7.3, shows the first occurring 5^{th} order Prime Number Associated Magic Cube for miscellaneous Magic Sums
The obtained results regarding the miscellaneous Prime Number Associated Magic Cubes as deducted and discussed in previous sections are summarized in following table: 
Order
Main Characteristics
Subroutine
Results
5
Associated, (Semi) Magic Surface Planes




Comparable routines as listed above, can be used to generate Prime Number Perfect Concentric Magic Cubes, which will be described in following sections.

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